A few comments are in order. Firstly, note that the minimal tree-level graviton-exchange term in \(f(s,u) \sim {1 \over s t u}\)  does not contribute to the sum rules of interest here, \(B_{k\ge 2}^+(s)\) . In particular, we are able to expand the sum rules in powers of \(s\) . Assuming a more stringent Regge bound, \(B^+_{1}(s)\)  can be studied [1]} and used to bound various coefficients in terms of \(G\) . We do not consider this sum rule in the present paper. Secondly, the non-minimal coupling \(\beta _{R^3}\)  contributes to \(B_2^+\)  and we utilize this fact in Sect. REF  in order to bound \(\beta _{R^3}\)  in terms of other EFT data.
